We choose \(\lambda \)  heuristically and we efficiently computed the minimum in \(\Psi ^{\lambda , L}(y^\delta )\)  by using the CGLS algorithm [1]}. We applied it to any corrupted datum \(y^\delta _i\) , and we stopped at iteration \(K\) , when one of the following conditions are satisfied:
\({\left\lbrace \begin{array}{ll}&||y^\delta - Ax^{(k)}||_2^2 < tol_f \\&||x^{(k)} - x^{(k-1)}||_2^2 < tol_x\end{array}\right.}\) 
